Mathematics-III

Origin of Partial Differential Equations, Linear and Non-Linear Partial Differential Equations of first order, Lagrange’s Equations method to solve Linear Partial Differential Equations, Charpit’s method to solve Non-Linear Partial Differential Equations, Solution of Linear Partial Differential Equation of Higher order with constant coefficients, Equations reducible to linear partial differential equations with constant coefficients.

Method of separation of variables, Solution of one dimensional heat equation, wave equation, Two dimensional heat equation (only Laplace Equation)and their application, Complex Fourier transform, Fourier sine transform, Fourier cosine transform, Inverse transform, convolution theorem, Application of Fourier Transform to solve partial differential equation.

Moments, Skewness, Kurtosis, Curve fitting, Method of least squares, Fitting of straight lines, Polynomials, Exponential curves, Correlation and regression, Binomial, Poisson and Normal distributions, Tests of significations: Sampling theory (small & large), Null hypothesis, Alternative hypothesis, testing of hypothesis: Chi-square test, t-test, z-test.

Zeroes of transcendental and polynomial equations using Bisection method, Regula-falsi method and Newton-Raphson method, Rate of convergence of above methods. Interpolation: Finite differences, Newton’s forward and backward interpolation, Lagrange’s and Newton’s divided difference formula for unequal intervals.

Numerical Techniques–II: 8 Solution of system of linear equations, Matrix Decomposition method, Jacobi method, Gauss- Seidel method. Numerical differentiation, Numerical integration, Trapezoidal rule, Simpson’s one third and three-eight rules, Solution of ordinary differential equations by Picard’s and fourth-order Runge-Kutta methods.